0,2

7*a(n)^2 - 5*b(n)^2 = 2 with companion sequence b(n)=A077416(n), n>=0.

a(n) = L(n,12), where L is defined as in A108299; see also A077416 for L(n,-12). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005

[a(n), A004191(n)] = the 2 X 2 matrix [1,10; 1,11]^(n+1) * [1,0]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 19 2008

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 12*a(n-1) - a(n-2), a(-1)=1, a(0)=1.

a(n) = S(n, 12) - S(n-1, 12) = T(2*n+1, sqrt(14)/2)/(sqrt(14)/2) with S(n, x) := U(n, x/2), resp. T(n, x), Chebyshev's polynomials of the second, resp. first, kind. See A049310 and A053120. S(-1, x)=0, S(n, 12)=A004191(n).

G.f.:(1-x)/(1-12*x+x^2).

a(n) = (ap^(2*n+1) + am^(2*n+1))/sqrt(14) with ap := (sqrt(7)+sqrt(5))/sqrt(2) and am := (sqrt(7)-sqrt(5))/sqrt(2).

a(n) = sqrt((5*A077416(n)^2 + 2)/7).

a(n)a(n+3) = 120 + a(n+1)a(n+2). - R. Stephan, May 29 2004

Cf. A072256(n) with companion A054320(n-1), n>=1.

Row 12 of array A094954.

Cf. A004191.

Sequence in context: A076255 A076357 A015606 this_sequence A082148 A075509 A061113

Adjacent sequences: A077414 A077415 A077416 this_sequence A077418 A077419 A077420

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002